Astro 1050     Mon. Oct. 21, 2002
   Today:  Review HW#6
Finish Ch. 9: Formation & Structure
Start Chapter 10: The Deaths of Stars

Homework #6
Q1.  The “Blade Runner Question.”  A star that burns half the lifetime of the sun does not burn twice as bright.  How bright (luminous) is it?
  Lifetime in solar units = M-2.5 (solar m)
0.5 = M-2.5
M2.5 = 2
M  =  (2)1/2.5 = 20.4= 1.3 solar masses
L in solar units = M3.5 (solar units)
Luminosity = (1.3)3.5 = 2.6 solar

Homework #6
Q2.  Spectroscopic parallax.  (Apparent) magnitude = 5.4 for an O6 V star.  How far away is it?  First need to get an absolute magnitude.  Can estimate it several ways (H-R diagrams, mass-luminosity relation).  I used M = -5.6.  So:
d (pc) = 10 (m-M+5)/5 = 103.2 = 1585 parsecs

Homework #6
Q3. Lava lamps display heat transport via CONVECTION.
Q4. EGGs in the Eagle Nebula are Evaporating Gaseous Globules.
Q5. Interstellar reddening occurs because dust preferentially scatters blue light, letting more of the red light through the cloud.

Lifetime on Main Sequence
L µ M3.5 T µ fuel / L = M/M3.5 = M-2.5
Example:  M=2 MSun      L = 11.3 LSun        T =1/5.7  TSun

Width of Main Sequence – and Stellar Aging
As star converts H to He you have more massive nuclei
Pressure related to number of nuclei
Gravity related to mass of nuclei
Pressure would tend to drop unless something else happens
Temperature must rise (slightly) to compensate
Luminosity  must  rise (slightly) as heat leaks out faster

Orion Nebula: A Star-Forming Region
Red light = Hydrogen emission
Blue light = reflection nebula
Dark lanes = dust
Astronomy Picture of the Day:

Protoplanetary Disks in the Orion Nebula
Dusty disk seen in silhouette
Central star visible at long wavelengths

Herbig-Haro objects: The angular momentum problem
As clouds try to collapse angular momentum makes them spin faster
A disk forms around the protostar
Material is ejected along the rotation axis

Herbig-Haro 34 in Orion
Jet along the axis visible as red
Lobes at each end where jets run into surrounding gas clouds

Motion of Herbig-Haro 34 in Orion
Can actually see the knots in the jet move with time
In time jets, UV photons, supernova, will disrupt the stellar nursery

Chapter 9 Summary
Interstellar Medium
Types of Nebulae (emission, reflection, dark)
Interstellar Reddening from dust
Star formation
Protostar Evolution on H-R Diagram
Fusion (CNO cycle, etc.)
Pressure-Temperature “Thermostat”
Stellar Structure (hydrostatic equilibrium, etc.)
Convection, radiation, and opacity
Stellar Lifetimes

Chapter 10 – The Deaths of Stars
What happens when the hydrogen runs out?
Star once again tries to contract and heat up inside
What might stop this?
“Unusual” fusion energy sources Ţ giant stars
Hydrogen shell fusion
Heavy element fusion
Degenerate electron pressure Ţ white dwarfs
Loss of material from the star

Hydrogen Shell Burning
Fusion stops in core when hydrogen runs out
Star has core of He, but T too low for fusion there
Heat loss makes star contract, T goes up in interior
Before T in core reaches He ignition point --
Hydrogen above He core begins “shell burning”
Shell burning changes the rules for structure
Still need dense core to allow high T, P for fusion
But high T on outside of core puts too much energy into outer parts of star
Outer parts responds to input energy by
expanding and cooling
Star in effect separates into two parts
Hot dense core where energy generation takes place
Extended envelope which shields and insulates core

Expansion into a Red Giant
For 5 MSun  “red giant”
Outer part swells to 75 RSun
Inner core still contains most of mass
Why is it red?
Two equivalent ways to answer:
Thick envelope insulates outside from hot core
L µ R2 T4 and
L  is not much greater (so far)
R2 is »(75/3)2 =252 = 625 times larger
T must decrease to compensate

HR Motion for other Mass Stars
For higher mass (already luminous) stars
Motion is more horizontal (to red)
Hard to increase luminosity above already very high levels

Motion in the HR Diagram
During H core burning (main sequence)
L increases slowly as He accumulates in the core (and TCore increases)
During H shell burning
At first R increases, T decreases
L then increases slowly as more He accumulates in core (and TCore increases)
Eventually He ignites in the core
During He core, H shell burning
Moving some of E generation back into core shrinks size (and so raises TSurface)
Eventually He in core runs out
 leaving a C, O core inside the He region
Core contracts and heats up till He ignites in shell outside C, O core
During He shell, H shell burning
At first R increases, TSurface decreases
L increases as more C,O accumulate and TCore continues to increase

Expected Evolution of the HR Diagram for a Cluster
A cluster consists of stars which all started to form at the same time  (collapsing from the same fragmenting molecular cloud)
Higher mass stars contract to main sequence before low mass ones reach it
Higher mass stars are also the first to run out of H and leave the main sequence, becoming supergiants.
As time continues, lower and lower mass stars move off the main sequence  (at the moving “turn off point”)

The original supergiants don’t live very long.
The lower mass stars produce giants

Tests of Stellar Evolution using the HR Diagram
Stellar evolution too slow to see changes in given cluster
Can observe clusters and look for predicted patterns

Complications in Stellar Evolution
Pressure forces other than thermal gas pressure
Reminder:  We’ve been assuming that when star loses energy it contracts and actually heats up.  Clearly not all objects do this (eg.  Earth)
Convection bringing in fuel from outer regions
Mass loss from stellar wind, or mass gain from nearby star

Pauli Exclusion Principle
From quantum rules, electrons don’t like to be packed into a small space, either in atoms or in ionized gas
At normal ionized gas densities, electrons are so spread out quantum rules don’t matter.
As high enough ionized gas densities, quantum rules need to be considered, just has they have been in atoms
Think of each “atom sized” region of space having a set of energy levels associated with it  (although it is really more complicated)

Effect of Degenerate Electron Pressure
Loss of energy does not reduce pressure
Star does not contract in response to loss of energy
Gravity not available as energy source to heat up star
Electrons are already in lowest energy states allowed
(equivalent to atoms in ground state) so no energy available there
If there is no other energy source, as energy is lost nuclei move slower and temperature drops.

Degenerate Pressure Can End Fusion
Degenerate Electron Pressure limits contraction and core temperature
“Stars” with M < 0.08 MSun never burn H    (brown dwarfs)
Stars    with M < 0.4   MSun never burn He   (red dwarfs)
Stars    with M < 4      MSun never burn C     (but do make red giants)
Stars    with M > 4      MSun do burn elements all the way to Fe
What happens to these objects?
Brown dwarfs never become bright – sort of like giant version of Jupiter
Red dwarfs have such long lives none have yet exhausted H
Red giants are related to white dwarfs
Massive stars explode as supernova

Effects of Convection
Energy can be moved by radiation or convection
Convection in core brings in new fuel
Cooler material more opaque
 making radiation harder and convection more likely
Choice also depends on energy flux

Mass Loss from Giant Stars
Envelope of red giant very loosely held
Star is so big, gravity very weak at the surface
Degenerate core makes nuclear “thermostat” sluggish
Core doesn’t quickly expand and cool when fusion is to fast
Energy can be generated in “thermal pulses”
Low temperature opaque envelope can also “oscillate”
Energy is transmitted in “pulses” as envelope expands and contracts
Main cause of “Variable Stars”

White Dwarfs

Simple Planetary Nebula
IC 3568   from the Hubble Space Telescope

Complicated P-N in a Binary System
M2-9 (from the Hubble Space Telescope)

A Gallery of P-N from Hubble

Complications in Binary Systems
Can move mass between stars
1st (massive) star becomes red giant
Its envelope transferred to other star
Hot (white dwarf) core exposed
2nd star becomes red giant
Its envelope transferred to white dwarf
Accretion disk around white dwarf
Angular momentum doesn’t let material fall directly to white dwarf surface
Recurrent nova explosions
White dwarf hot enough for fusion, but no Hydrogen fuel
New fuel comes in from companion
Occasionally ignites explosively,
 blowing away remaining fuel

Is a star stable against catastrophic collapse?
Imagine compressing a star slightly (without removing energy)
Pressure goes up (trying to make star expand)
Gravity also goes up (trying to make star collapse)
Does pressure go up faster than gravity?
If Yes:  star is stable – it bounces back to original size
If No:   star is unstable – gravity makes it collapses
Ordinary gas: P does go up fast –  stable
Non-relativistic degenerate gas:   P does go up fast –  stable
Relativistic degenerate gas: P does not go up fast –  unstable
Relativistic:   Mean are the electrons moving at close to the speed of light
Non-relativistic degenerate gas:   increasing r means not only more electrons, but faster electrons, which raises pressure a lot.
Relativistic degenerate gas:   increasing r can’t increase electron velocity (they are already going close to speed of light) so pressure doesn’t go up as much

Chandrasekhar Limit for White Dwarfs
Add mass to an existing white dwarf
Pressure (P) must increase to balance stronger gravity
For degenerate matter, P depends only on density (r), not temperature, so must have higher density
P vs. r rule such that higher mass star must actually have smaller radius to provide enough P
As Mstar ® 1.4 MSun      velectron ® c
Requires much higher r to provide high enough P, so star must be much smaller.
Strong gravity which goes with higher r makes this a losing game.
For M ł 1.4 MSun no increase in r can provide enough increase in P – star collapses

Implications for Stars
Stars less massive than 1.4 MSun can end as white dwarfs
Stars more massive than 1.4 MSun can end as white dwarfs, if they lose enough of their mass (during PN stage) that they end up with less than 1.4 MSun
Stars whose degenerate cores grow more massive than 1.4 MSun will undergo a catastrophic core collapse:
Neutron stars

When the degenerate core of a star exceeds 1.4 MSun it collapses
Type II:  Massive star where it runs out of fuel after converting core to Fe
Type  I:  White dwarf in binary, which receives mass from its companion.
Star’s core begins to collapse
Huge amounts of gravitational energy liberated
Extreme densities allows weak force to convert matter to neutrons
p+ + e-
®  n + n
Neutrinos (n) escape, carrying away much of energy, aiding collapse
Collapsing outer part is heated, “bounces” off core, is ejected into space
Light from very hot ejected matter makes supernova very bright
Ejected matter contains heavy elements from fusion and neutron capture
Core collapses into either:
Neutron stars or Black Holes (Chapter 11)

Supernova in Another Galaxy
Supernova 1994D in NGC 4526

Tycho’s Supernova of 1572
Now seen by the Chandra X-ray Observatory as an expanding cloud.

The Crab Nebula – Supernova from 1050 AD
Can see expansion between 1973 and 2001
Kitt Peak National Observatory Images

What happens to the collapsing core?
Neutron star (more in next chapter)
Quantum rules also resist neutron packing
Densities much higher than white dwarfs allowed
R ~ 5 km      r ~ 1014 gm/cm3   (similar to nucleus)
M limit uncertain,  ~2 or ~3 MSun before it collapses
Spins very fast (by conservation of angular momentum)
Trapped spinning magnetic field makes it:
Act like a “lighthouse” beaming out E-M radiation (radio, light)
Accelerates nearby charged particles

Spinning pulsar powers the
 Crab nebula
Red:  Ha
Blue:  “Synchrotron” emission from high speed electrons trapped in magnetic field

Review Chapters 7-10
Chapter 7: The Sun
Atmospheric Structure
Sunspots/Magnetic Phenomena
Nuclear Fusion – proton-proton chain
Solar Neutrino “Problem”

Review Chapters 7-10
Chapter 8: The Properties of Stars
Distances to Stars
Parallax and Parsecs
Spectroscopic Parallax
Intrinsic Brightness: Luminosity
Absolute Magnitude
Luminosity, Radius, and Temperature
Hertzsprung-Russell (H-R) Diagram
Luminosity Classes (e.g., Main Sequence, giant)
Masses of Stars
Binary Stars and Kepler’s Law
Mass-Luminosity Relationship

Review Chapters 7-10
Ch. 9: The Formation & Structure of Stars
Interstellar Medium
Types of Nebulae (emission, reflection, dark)
Interstellar Reddening from dust
Star formation
Protostar Evolution on H-R Diagram
Fusion (CNO cycle, etc.)
Pressure-Temperature “Thermostat”
Stellar Structure (hydrostatic equilibrium, etc.)
Convection, radiation, and opacity
Stellar Lifetimes

Review Chapters 7-10
Ch. 10: The Deaths of Stars
Evolution off the main sequence (=> giant)
Star Cluster Evolution on H-R Diagram
Degenerate Matter
Planetary Nebulae and White Dwarfs
Binary Star Evolution (Disks, Novae, etc.)
Massive Star Evolution and Supernovae